Cluster Groups

WS 2017/2018

Graph Theory

Reading Spectral graph theory by Fan R. K. Chung

  • Chapter 2: Isoperimetric problems
  • Chapter 3: Diameters and eigenvalues
  • Talk by Anna Muranova: On effective resistance of electric network with impedances
  • Talk by Melissa Meinert: Ollivier Ricci curvature for general Laplacians
  • Markov chains
  • Talk by Filip Bosnic: Examples of Poincaré and log-Sobolev inequalities on discrete configuration spaces
  • Introduction to random graphs by Alan Frieze and Michał Karoński

Lévy processes

Discuss Lévy Processes and Infinitely Divisible Distributions by Ken-iti Sato

  • Chapter 1 (pp. 1 - 30): Examples of Levy Processes
  • Chapter 2 (pp. 31 - 68): Characterisation and Existence of Levy Processes and Additive Processes
  • Chapter 2 (pp. 31 - 41): Infinitely Divisible Processes and the Lévy-Khintchine formula
  • Chapter 2 (pp. 54 - 67): Transition Functions and the Markov Property; Existence of Lévy and Additive Processes
  • Chapter 3 (pp. 69 - 77): Selfsimilar and Semi-selfsimilar Processes and their Exponents
  • Chapter 3 (pp. 77 - 90): Representations of Stable and Semi-stable Distributions
  • Viswanathan et al. Papers: “Levy Flight Search Patterns of Wandering Albatrosses” and “Optimizing the Success of Random Searches”
  • Bertoin (pp. 18-24): Potential theory: Markov property and important definitions
  • Bertoin (pp. 43-48): Duality and time reversal
  • Bertoin (pp. 48-56): Potential theory: capacity measure; essentially polar sets and capacity
  • Bertoin (pp. 56-68): Potential theory: energy; the case of a single point
  • Bertoin (pp. 71-84): Subordinators: definitions; passage across a level; arcsine laws
  • Bertoin (pp. 84-99): Subordinators: rates of growth; (Hausdorff-)dimension of the range

Analysis

Discuss

  • Maximum principle for ecliptic operators (Gibarg-Trudinger)
  • Paley-Littlewood Decomposition (Grafakos classical Fourrier Analysis, second or third edtion)
  • Another looks at Sobolev spaces (Articles Brezis Bourgain_Mironescu)
  • Spectral theory: spectral measure for Unbounded operators
  • Spectral theory for unbounded operator and spectral measure (Book by Reed-Simon)
  • Restriction of the Fourier Transform on the sphere (Book by Elias Stein)
  • Interplation of Banach spaces and application (Lecture note by Alessandra Lunadri Theory of interpolation 2009)
  • Introduction to optimal transport theory (Book by Cedri Villani: Old and New, it is free on-line)
  • Introduction to control and non linearity (Book by Jean-Michel Coron: Control and Non-linearity free one his we-page)
  • Introduction to Calculus of variations

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